Geometric Stiffening and Softening of an Indented Floating Thin Film*

Thin sheets can behave nonlinearly while the local material response is purely linear. We separate two distinct mechanisms for geometric nonlinearities by studying the normal-force response of an indented polymer film on a liquid bath, using experiments, simulations, and theory. First, we show that the force reaches a plateau at large indentation, causing the effective spring constant of the system to soften, and we use a simple geometric model to capture this behavior at large slopes [1]. Then, we map out the full phase diagram at small slopes, supporting recent predictions [2] that the system stiffens out of the typical linear response for small deflections. Our results provide a prototypical example of how multiple distinct geometric nonlinearities may arise under monotonic driving.
[1] Ripp et. al., arXiv:1804.02421 (2018)
[2] Vella et al., Phys. Rev. E 98, 013003 (2018)